Question 1$1$: Retail Inventory Management

A chain of retail stores operates in various locations, each with different demand patterns and inventory storage costs. The goal is to optimize the distribution of products to minimize costs and balance stock levels while considering constraints on available inventory.

a.$.$ How can the retail chain formulate and solve an LP model ($($using the Northwest corner approach)$)$ to optimize inventory distribution, accounting for storage costs at different stores and considering the interplay between cost minimization and inventory constraints?

(10$(10$ marks)$)$

b.$.$ How does including storage costs at stores impact the objective function?

(10$(10$ marks)$)$

c.$.$ In what ways can the LP model be extended to address multi−$-$objective optimization, potentially considering other factors such as carbon emissions or supply chain resilience? (10$(10$ marks)$)$

Store1$1$ Store2$2$ Store3$3$ Store4$4$ Storage Cost Supply

Product1100801209051500$1100801209051500$

Product212010014011062000$212010014011062000$

Product315013017014072500$315013017014072500$

Demand 500600800700$500600800700$